Question

Consider a matrix $A\left(\theta \right)\left[\begin{array}{c}sin\theta cos\theta \\ -\cos \theta \sin \theta \end{array}\right]$ then

Answer 1

$\begin{array}{c}Then,Itserminent\\ \Rightarrow A\left(\theta \right)=\left|\begin{array}{cc}\sin \theta & \cos \theta \\ -\cos \theta & \sin \theta \end{array}\right|\\ \Rightarrow \left|A\left(\theta \right)\right|={\sin }^2\theta +{\cos }^2\theta \\ \Rightarrow \left|A\left(\theta \right)=1\right|\end{array}$